The desire to pin down who she was (and the fact that Marie was a very common name) has led to numerous guesses regarding her identity, none of which would make a difference in the study of her writings. (If Shakespeare's plays were written by the Earl of Oxford, how would that change our enjoyment of them? Not a bit.)
Those who have heard of her know of The Lais of Marie de France, a collection 12 lais. A lai (English lay) was a lyric poem in octosyllabic couplets, popular in France and Germany in the 13th and 14th centuries, dealing with adventure and romance. The 12 are written in Anglo-Norman and often focus often on courtly love. A few of the stories exist separately in manuscripts, but there is one manuscript in the British Library that has all 12. That manuscript, Harley 978, presents them in what may be a deliberate order: the odd numbers show positive results for characters who love others; the even lais show the negative results of love that is imperfect. (Bisclavret is number four, an even number.)
Harley 978 also has a prologue in which we gain some insight into Marie. She writes that she wanted to create something that would be entertaining and morally instructive in the style of Greco-Roman literature. She therefore is recording Breton tales that she has learned. The prologue also dedicates the lais to a "noble king." From the time period in which they seem to be written, and her knowledge of Anglo-Norman and Middle English, the assumption is that she was known in the court of Henry II or possibly even his son.
A few other works are also attributed to her. She is credited with a retelling of the Legend of the Purgatory of St. Patrick, a French translation of a latin poem. "Purgatory" in this case is not a cosmic status between Heaven and Hell; it is a pilgrimage site in Northern Ireland, a cave that Christ showed to St. Patrick and explained was an entrance to Purgatory.
She also produced a re-telling of Aesop's Fables called Ysopet ("Little Aesop"), which has some fables not seen in Aesop. Many of her fables are about humans, and in many of those she presents tales of female cunning over male ignorance or foolishness.
Her fables would make a good topic on their own, so that's what we will look at next.